Filtering is a fundamental signal processing tool used in almost all electronic systems. While some filtering functions can be performed in the digital domain, filtering in the analog domain is essential in countless applications where only analog techniques enable high-speed processing of small signal levels with the required resolution. Front-end processing in almost all electronic systems such as wireless and wireline communications, video, audio, imaging, etc. rely heavily on filtering in the analog domain.
We have been witnessing in the last several decades that the cost and footprint of electronic systems are scaling down significantly as increasingly more functionality is integrated on a single chip of semiconductor. While microchip processing is extremely efficient in building a large number of devices on a microchip, analog processing still suffers from variations in component values from one fabrication run to another. Further limitations to analog processing accuracy come from the dependence of component parameters on temperature, which is becoming more and more costly to control as a result of larger scale integration. A widely recognized solution to this problem is the tuning of on-chip components until the error due to component variations becomes negligible.
In a typical RC filter composed of amplifiers, resistors and capacitors, the accuracy of the filter transfer function is determined by the resistor and capacitor values. In general, either resistors or capacitors can be tuned to obtain the required overall transfer function. Tuning can be performed efficiently by switching small-valued components in or out of the circuit. As the dominant non-ideality of a reasonably-sized micro-switch is its parasitic resistance (up to very high frequencies), tuning of capacitors poses a difficulty as a result of an undesired resistance appearing in series with the capacitor to be tuned. Tuning of resistors, therefore, can be more effective in many realizations.
FIG. 1 illustrates an exemplary low pass filter 100. Low pass filter 100 may be tuned by adjusting the value of the resistor components. Low pass filter 100 comprises operational amplifier 120 having an input resistor R1 coupled to the inverting input of operational amplifier 120. Resistor R2 and capacitor C are coupled in parallel with operational amplifier 120 as shown in FIG. 1. As is well known in the art, the transfer function of low pass filter 100 is given by the expression:                                           V            out                                V            in                          =                                            -              R2                        R1                    ⁢                      (                          1                              1                +                sCR2                                      )                                              (        1        )            As the value of resistor R2 and the value of capacitor C are varied, the value of the pole of the filter (equal to the reciprocal of CR2) also varies.
If the resistor R2 is tunable, then the value of resistor R2 can be adjusted to compensate for process variations of both R2 and C. For example, if the value of capacitor C was twenty percent (20%) below its nominal value, then the value of resistor R2 could be tuned to twenty five percent (25%) above its nominal value in order to compensate. That is,(0.80 C nominal) (1.25 R2 nominal)=(1.00) (CR2 nominal).
However, in order to keep the gain constant, resistor R1 would also have to be tuned in the same way as resistor R2. Otherwise, the value of the gain term (−R2/R1) would not remain constant. It is therefore desirable to tune both resistor R1 and resistor R2 in a manner that ensures that their matching remains good. In more complicated filters, additional resistors would also need to be tuned. It is desirable that the respective ratios of such resistors also remain constant.
FIG. 2 illustrates a conventional prior art circuit 200l for tuning a resistor by switching in or out some small-valued resistors that are in series with the resistor to be tuned (RTUNE). Switches S in circuit 200 are closed and opened to include more or less resistance RX in series with the resistance to be tuned. When fine tuning is desired, the switched resistors need to be much smaller than the resistor to be tuned, typically on the order of one hundredth (0.01) or less. This necessarily requires large size switches, such that the parasitic switch resistance can be neglected next to the tuning resistors.
A typical example is a five thousand ohm (5 kΩ) resistor to be tuned to below one percent (1%) precision. This requires tuning resistors that are less than fifty ohms (50 Ω), which in turn requires a switch resistance on the order of ten ohms (10 Ω) or less. A switch with such a low on resistance requires a transistor that is several hundred times larger than a minimum geometry device. Note that, increased switch size, besides requiring more chip real estate, also exhibits higher parasitic capacitance along the signal path, and increased noise coupling through the substrate. The large spread of resistor values also limits the accuracy and matching between resistors. Small-valued resistors also require much more hand-tailoring in layout, as their aspect ratios turn out to be awkward, and parasitic contact resistances introduce considerable error to the overall resistance. Another difficulty is that different tuning resistor values are needed for each different resistor value to be tuned (so that the same relative accuracy can be maintained across all resistors). For example, fifty ohm (50 Ω) resistors are needed to tune a five thousand ohm (5 kΩ) resistance, whereas seventy five ohm (75 Ω) resistors would be needed to tune a seven thousand five hundred ohm (7.5 kΩ) resistor with the same relative increments.
There is therefore a need in the art for an improved apparatus and method for tuning a resistor in an electronic circuit. In particular, there is a need in the art for an improved apparatus and method for tuning a resistor in an on-chip, microelectronic component such as an RC filter.